Estimation of parameter confidence using Monte Carlo integration. (A) The estimate of confidence from Eq. 9 as a function of the number of posterior samples, $θ˜,$ used for Monte Carlo integration. This estimate converges quickly. (B) Confidence as a function of sample size estimated using a point estimate of θ (⁠$αθˆ$⁠) and the Bayesian estimate (α_B). It is clear that $αθˆ$ overestimates parameter confidence and that the true uncertainty in θ must be taken into account for an accurate estimate of confidence.